I have yet to find mention of the monetary value of a dog at Red River, but there is plenty of evidence that people placed a high value on their dogs.

There were other purposes for dogs. In August of 1812, Miles Macdonell writes about Fort Alexander that, although it was on a river (the Winnipeg) key to commerce, the river “was a scarce place for provisions. The Canadians killed two dogs for their supper.”
The winter of 1825-6 was a bitter winter. The Bison disappeared, and travel across the massive drifts of snow was nearly impossible. Dogs became a part of the diet of the starving colonists.

There is no question that dogs were essential to life at Red River. But their working days were mostly winter days. These were hardy dogs, fit and perhaps high-strung – in terms of energy, at least. So, the major problems began when the snow and ice disappeared and the main method of dissipating all that energy melted away with the arrival of spring.